1. Field of the Invention
The invention relates to a Global Positioning System, and in particular, to a GPS acquisition method for use in weak signal environments.
2. Description of the Related Art
FIG. 1 shows a sequence of data bits with bit-transition. In a Global Positioning System (GPS) receiver, transmission signals are demodulated and digitized into a sequence of data bits. According to GPS L2 civil signal standard, a bit value sustains for a period, such as 20 ms for L2 civil moderate (CM) maximal length code. Bit transition may therefore occur every 20 ms. Pseudo-random number (PRN) codes and carrier signals sent from several GPS satellites must be acquired and tracked for use. A typical receiver channel operates in two modes: acquisition and tracking. In acquisition mode, PRN code phase (measured by start time of the PRN code) and carrier Doppler offset are estimated via a search process. The estimated quantities are then used and continuously updated in tracking mode.
FIG. 2 shows a search space m(n) formed by presumed code phases and presumed offsets. A received GPS signal is typically defined as follows:r(t)=√{square root over (A)}·N(t)·s(t−τ)·ej2πfdt+n(t)  (1)
The parameter A represents the power of the received GPS signal. N(t) denotes a navigation bit value at time t. Each bit value has a span (bit period) of 20 ms. τ is an unknown code phase to be determined. fd is an unknown Doppler offset value in KHz. n(t) is an assumed additive white Gaussian noise (AWGN).
If the received GPS signal r(t) is digitized at a 5 MHz sample rate, 5000 samples are available per 1 ms. For most applications, frequency range of the received signal with Doppler offset falls within ±10 KHz with respect to a center frequency 1250 KHz. To simplify the search for Doppler offset value, the frequency range is coarsely sliced into 21 presumed values, −10 to 10 KHz with a step size of 1 KHz. The search space m(n) is therefore formed to determine the unknown code phase and the unknown Doppler offset value forcibly:m(n)={yi,j(n)|i,jεR,1≦i≦p,1≦j≦q}  (2)
The parameter n denotes an nth bit period, and the nth search space m(n) comprises p*q elements where the amount of possible code phases p is 5000, and the amount of possible offset values q is 21. yi,j(n) is a correlation value corresponding to an (ith, jth) element calculated per code time:
                                          y                          i              ,              j                                ⁡                      (            n            )                          =                              ∫                                          (                                  n                  -                  i                                )                            ⁢              T                        nT                    ⁢                                    r              ⁡                              (                t                )                                      ⁢                                          s                ⁡                                  (                                      t                    -                                          τ                      i                                                        )                                            ·                              ⅇ                                  j                  ⁢                                                                          ⁢                  2                  ⁢                  π                  ⁢                                                                          ⁢                                      f                    j                                    ⁢                  t                                                      ⁢                          ⅆ              t                                                          (        3        )            
The parameter T represents the code time (1 ms for this case). τi is the ith presumed code phase, and fj is the jth presumed offset. A total of 5000*21 correlation values are simultaneously calculated within 1 ms, and a peak can be found, with corresponding code phase and offset value thereof used as the acquisition result.
In high SNR situations (e.g. outdoors or in rural areas), the 1-ms correlation is generally satisfactory for detecting code phase and Doppler offset. For weak signal environments (low SNR situation), however, the correlation results yi,j(n) are typically accumulated for multiple periods before selection of a peak as an answer, such that possibility of false detection is reduced. Various conventional accumulation algorithms are readily presented, such as coherent combination (CC), non-coherent combination (NCC) and differential-coherent combination (DCC).
FIG. 3 shows an integral calculated by a conventional coherent combination algorithm. The coherent combination algorithm is presented as:
                              P          CC          N                =                  max          ⁢                      {                                                                                                ∑                                          n                      =                      1                                        N                                    ⁢                                                            y                                              i                        ,                        j                                                              ⁡                                          (                      n                      )                                                                                                  2                        }                                              (        4        )            
Correlation values yi,j(n) corresponding to the (ith, jth) element are accumulated for consecutive code times 1 to N, and their sums squared before selection of a peak therefrom. The coherent combination algorithm provides excellent accuracy for peak detection without squaring loss. As a result of the navigation bit-transition periodically occurring as shown in FIG. 1, however, the integral may be deteriorated. As shown in FIG. 3, a coherent combination integral of a (ith, jth) element in the search space is also referred to as an element value of a corresponding correlation value yi,j(n). The horizontal axis denotes the integration time N (the unit is referred to as code time). The element value grows before the bit-transition occurring at N=10 and 30, and decreases thereafter due to a cancellation effect induced by complex number operations in formula (3). As seen, the element value cannot effectively increase to distinguish a peak from noise.
The non-coherent combination algorithm is denoted as follows:
                              P          NCC          N                =                  max          ⁢                      {                                          ∑                                  n                  =                  1                                N                            ⁢                                                                                                            y                                              i                        ,                        j                                                              ⁡                                          (                      n                      )                                                                                        2                                      }                                              (        5        )            
Based on the non-coherent combination (NCC) algorithm, absolute values are taken before summation, alleviating the bit-transition cancellation problem. As SNR decreases, however, an element value calculated from the non-coherent combination algorithm may suffer from squaring loss, making it impractical for weak signal environment. Therefore, a more flexible combination scheme is desirable in GPS acquisition.